How do you write x³+7x²+10x in factored form?

1 Answer
May 1, 2018

x(x+2)(x+5)

Explanation:

First, we can factor out x, because all of the terms of the polynomial include x:
=x(x^2+7x+10) Now, looking at (x^2+7x+10):
Since the x^2 term's coefficient is one, we know the factoring will look something like:
(x+-a)(x+-b). Looking at the other terms of the polynomial, we see that factors of 10 will have to add up to 7 (both are positive so both signs will be positive. Factors of 10:
(1,10)
(2,5)
And after this, it's the same in the opposite order. We can see that 2+5=7, so 2 and 5 must go in to the equation:
(x+2)(x+5). Inputting this into the other we get:
x(x+2)(x+5)